Derivation of the Existence of an Upper Limit to Sequence Identity Required to Maintain Replication Function
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901748526874624 |
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| author | miyamoto, ikutoshi |
| author_facet | miyamoto, ikutoshi |
| contents | <p>In this study, we derive the critical sequence identity Q required to maintain replication<br>function in a minimal model of early life. Unlike classical quasispecies models that assume<br>a static fitness landscape, our model evaluates fitness based on relative similarity to the<br>immediate parent (a moving reference frame).<br>Using the Poisson approximation to the binomial mutation count, we obtain the exact<br>condition for the critical threshold Q as follows:<br>Q = max {q ∈ 0, 1/n , 2/n , ..., 1 | Γ (1 + n − nq, np) /Γ (1 + n − nq) = 1/2}.<br>where Γ (a, x) is the upper incomplete gamma function.<br>This result implies that the required sequence identity per generation must be at most<br>the limit set by Q. In the regime where the expected number of mutations np is sufficiently<br>large, this analytical threshold simplifies to Q ⋍ 1 - p. Consequently, the fact that there is<br>an upper limit (Q) to the identity required to maintain replication suggests that lineages<br>must tolerate ongoing divergence to persist.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18763658 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Derivation of the Existence of an Upper Limit to Sequence Identity Required to Maintain Replication Function miyamoto, ikutoshi Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome Biological sciences Relative Fidelity Moving Reference Frame <p>In this study, we derive the critical sequence identity Q required to maintain replication<br>function in a minimal model of early life. Unlike classical quasispecies models that assume<br>a static fitness landscape, our model evaluates fitness based on relative similarity to the<br>immediate parent (a moving reference frame).<br>Using the Poisson approximation to the binomial mutation count, we obtain the exact<br>condition for the critical threshold Q as follows:<br>Q = max {q ∈ 0, 1/n , 2/n , ..., 1 | Γ (1 + n − nq, np) /Γ (1 + n − nq) = 1/2}.<br>where Γ (a, x) is the upper incomplete gamma function.<br>This result implies that the required sequence identity per generation must be at most<br>the limit set by Q. In the regime where the expected number of mutations np is sufficiently<br>large, this analytical threshold simplifies to Q ⋍ 1 - p. Consequently, the fact that there is<br>an upper limit (Q) to the identity required to maintain replication suggests that lineages<br>must tolerate ongoing divergence to persist.</p> |
| title | Derivation of the Existence of an Upper Limit to Sequence Identity Required to Maintain Replication Function |
| topic | Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome Biological sciences Relative Fidelity Moving Reference Frame |
| url | https://doi.org/10.5281/zenodo.18763658 |